NOTE: this is not Fisher's equation in differential equations

The Fisher equation in financial mathematics estimates the relationship between nominal and real interest rates under inflation. This equation is primarily used in YTM calculations of bonds or IRR calculations of investments.

Let <math>r_r<math> denote the real interest rate, <math>r_n<math> denote the nominal interest rate, and let <math>\pi<math> denote the rate of inflation.

The Fisher equation is the following:

<math>r_n = r_r + \pi<math>

The equation can be used in either ex-ante (before) or ex-post (after) analysis.

This equation is named after Irving Fisher who was famous for his works on the theory of interest. This equation existed before Fisher, but Fisher proposed a better approximation which is given below. The estimated equation can be derived from the proposed equation

<math>1 + r_n = (1 + r_r)(1 + \pi).<math>

Derivation

From

<math>1 + r_n = (1 + r_r)(1 + \pi)<math>

follows

<math>1 + r_n = 1 + r_r + \pi + r_r \pi

and hence

Drop <math>r\pi<math> because <math>r + \pi<math> is much larger than <math>r\pi<math>:

<math>i = r + \pi<math>

is the result.

See also

• yield
• interest rate, inflation
• Term Structure of Interest Rates
• Fisher hypothesis